but when I look at my domain I see empty page, but looking in page source I see something like this:

<!DOCTYPE html>
<html>
<head>
<title>Welcome to nginx!</title>

It seems Docker is using default Nginx file and takes only part of it (probably the exact length of it as it is in my index.html file. With other files for example abc.html there’s no such issue (probably because it does not exist by default in Nginx image). How can I solve this issue to display correct content of index.html file ?

As your volume starts with /c/..., I’m assuming that you’re using the Docker Toolbox on Windows and the docker-machine tool shipped with it. What you’re experiencing is a known issue of Nginx (or rather the sendfile Linux system call that Nginx uses) in conjunction with Virtualbox shared folders.

This issue is also mentioned in the Vagrant documentation (which also uses VirtualBox), which also comes with a suggested solution that might work for you:

There is a VirtualBox bug related to sendfile which can result in corrupted or non-updating files. You should deactivate sendfile in any web servers you may be running.

In Nginx:

sendfile off;

In Apache:

EnableSendfile Off

According to the latest comments in the bug report in the vendor bug tracker, if you’re using the open_file_cache directive (disabled by default), you’ll need to turn that off, too: